Solve for $x$ : $2\sqrt{x} - 1 = 10\sqrt{x} + 5$
Solution: Subtract $2\sqrt{x}$ from both sides: $(2\sqrt{x} - 1) - 2\sqrt{x} = (10\sqrt{x} + 5) - 2\sqrt{x}$ $-1 = 8\sqrt{x} + 5$ Subtract $5$ from both sides: $-1 - 5 = (8\sqrt{x} + 5) - 5$ $-6 = 8\sqrt{x}$ Divide both sides by $8$ $\frac{-6}{8} = \frac{8\sqrt{x}}{8}$ Simplify. $-\dfrac{3}{4} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.